TSTP Solution File: NUM743^4 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM743^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 08:57:04 EDT 2024
% Result : Theorem 90.13s 11.95s
% Output : CNFRefutation 90.50s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_23,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
in: $i > $i > $o ).
thf(decl_27,type,
emptyset: $i ).
thf(decl_42,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(decl_49,type,
omega: $i ).
thf(decl_58,type,
ap: $i > $i > $i ).
thf(decl_60,type,
d_Pi: $i > ( $i > $i ) > $i ).
thf(decl_61,type,
imp: $o > $o > $o ).
thf(decl_62,type,
d_not: $o > $o ).
thf(decl_67,type,
l_or: $o > $o > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_127,type,
n_some: ( $i > $o ) > $o ).
thf(decl_147,type,
diffprop: $i > $i > $i > $o ).
thf(decl_148,type,
d_29_ii: $i > $i > $o ).
thf(decl_149,type,
iii: $i > $i > $o ).
thf(decl_161,type,
times: $i > $i ).
thf(decl_162,type,
n_ts: $i > $i > $i ).
thf(decl_167,type,
d_1to: $i > $i ).
thf(decl_172,type,
n_2: $i ).
thf(decl_176,type,
pair1type: $i > $i ).
thf(decl_178,type,
first1: $i > $i > $i ).
thf(decl_179,type,
second1: $i > $i > $i ).
thf(decl_189,type,
frac: $i ).
thf(decl_191,type,
num: $i > $i ).
thf(decl_192,type,
den: $i > $i ).
thf(decl_193,type,
n_eq: $i > $i > $o ).
thf(decl_194,type,
moref: $i > $i > $o ).
thf(decl_195,type,
lessf: $i > $i > $o ).
thf(decl_197,type,
lesseq: $i > $i > $o ).
thf(decl_198,type,
epred1_2: $i > $i > $o ).
thf(decl_199,type,
epred2_2: $i > $i > $o ).
thf(decl_200,type,
epred3_2: $i > $i > $o ).
thf(decl_201,type,
epred4_2: $i > $i > $o ).
thf(decl_202,type,
epred5_2: $i > $i > $o ).
thf(decl_208,type,
esk1_0: $i ).
thf(decl_209,type,
esk2_0: $i ).
thf(decl_210,type,
esk3_0: $i ).
thf(def_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X1: $i] : ( X1 != emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_nat) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_l_or) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_d_not) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_n_eq) ).
thf(def_num,axiom,
( num
= ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_num) ).
thf(def_den,axiom,
( den
= ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_den) ).
thf(def_n_ts,axiom,
( n_ts
= ( ^ [X1: $i] : ( ap @ ( times @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_n_ts) ).
thf(def_lessf,axiom,
( lessf
= ( ^ [X1: $i,X450: $i] : ( iii @ ( n_ts @ ( num @ X1 ) @ ( den @ X450 ) ) @ ( n_ts @ ( num @ X450 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_lessf) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_iii) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_is_of) ).
thf(def_moref,axiom,
( moref
= ( ^ [X1: $i,X449: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X449 ) ) @ ( n_ts @ ( num @ X449 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_moref) ).
thf(def_pair1type,axiom,
( pair1type
= ( ^ [X1: $i] :
( d_Pi @ ( d_1to @ n_2 )
@ ^ [X425: $i] : X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_pair1type) ).
thf(def_lesseq,axiom,
( lesseq
= ( ^ [X1: $i,X466: $i] : ( l_or @ ( lessf @ X1 @ X466 ) @ ( n_eq @ X1 @ X466 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_lesseq) ).
thf(def_frac,axiom,
( frac
= ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',def_frac) ).
thf(satz41d,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X469: $i] : ( in @ X469 @ frac )
@ ^ [X470: $i] :
( ( lesseq @ X1 @ X470 )
=> ( d_not @ ( moref @ X1 @ X470 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz41d) ).
thf(satz37,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] : ( n_eq @ X1 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz37) ).
thf(satz51b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X495: $i] : ( in @ X495 @ frac )
@ ^ [X496: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( lessf @ X1 @ X496 )
=> ( ( lesseq @ X496 @ X4 )
=> ( lessf @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz51b) ).
thf(satz41g,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X475: $i] : ( in @ X475 @ frac )
@ ^ [X476: $i] :
( ( moref @ X1 @ X476 )
=> ( d_not @ ( lesseq @ X1 @ X476 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz41g) ).
thf(satz41k,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X481: $i] : ( in @ X481 @ frac )
@ ^ [X482: $i] :
( ( d_not @ ( lesseq @ X1 @ X482 ) )
=> ( moref @ X1 @ X482 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz41k) ).
thf(satz50,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X491: $i] : ( in @ X491 @ frac )
@ ^ [X492: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( lessf @ X1 @ X492 )
=> ( ( lessf @ X492 @ X4 )
=> ( lessf @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz50) ).
thf(satz42,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X457: $i] : ( in @ X457 @ frac )
@ ^ [X458: $i] :
( ( moref @ X1 @ X458 )
=> ( lessf @ X458 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz42) ).
thf(satz43,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X459: $i] : ( in @ X459 @ frac )
@ ^ [X460: $i] :
( ( lessf @ X1 @ X460 )
=> ( moref @ X460 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz43) ).
thf(satz41e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X471: $i] : ( in @ X471 @ frac )
@ ^ [X472: $i] :
( ( d_not @ ( moref @ X1 @ X472 ) )
=> ( lesseq @ X1 @ X472 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz41e) ).
thf(satz45,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X463: $i] : ( in @ X463 @ frac )
@ ^ [X464: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( all_of
@ ^ [X13: $i] : ( in @ X13 @ frac )
@ ^ [X13: $i] :
( ( lessf @ X1 @ X464 )
=> ( ( n_eq @ X1 @ X4 )
=> ( ( n_eq @ X464 @ X13 )
=> ( lessf @ X4 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz45) ).
thf(satz51a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X493: $i] : ( in @ X493 @ frac )
@ ^ [X494: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( lesseq @ X1 @ X494 )
=> ( ( lessf @ X494 @ X4 )
=> ( lessf @ X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p',satz51a) ).
thf(c_0_26,plain,
( nat
= ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[def_nat]) ).
thf(c_0_27,plain,
( l_or
= ( ^ [Z0: $o] : ( imp @ ( imp @ Z0 @ ~ $true ) ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_28,plain,
( d_not
= ( ^ [Z0: $o] : ( imp @ Z0 @ ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_29,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_30,axiom,
( num
= ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[def_num,c_0_26]) ).
thf(c_0_31,axiom,
( den
= ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[def_den,c_0_26]) ).
thf(c_0_32,plain,
( n_ts
= ( ^ [Z0: $i] : ( ap @ ( times @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_ts]) ).
thf(c_0_33,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_34,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( n_some @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_35,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_36,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_37,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moref]) ).
thf(c_0_38,plain,
( pair1type
= ( ^ [Z0: $i] :
( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_pair1type]) ).
thf(c_0_39,plain,
( lesseq
= ( ^ [Z0: $i,Z1: $i] :
( imp
@ ( imp
@ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) ) ) )
@ ~ $true )
@ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lesseq]) ).
thf(c_0_40,plain,
( l_or
= ( ^ [Z0: $o] : ( imp @ ( imp @ Z0 @ ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_41,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]) ).
thf(c_0_42,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] :
( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_30]),c_0_31]),c_0_32]),c_0_34]) ).
thf(c_0_43,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_44,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] :
( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_37,c_0_30]),c_0_31]),c_0_32]) ).
thf(c_0_45,axiom,
( frac
= ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[def_frac,c_0_26]),c_0_38]) ).
thf(c_0_46,plain,
( lesseq
= ( ^ [Z0: $i,Z1: $i] :
( imp
@ ( imp
@ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) ) ) )
@ ~ $true )
@ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z2: $i] : ( Z2 != emptyset ) )
@ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42]) ).
thf(c_0_47,plain,
! [X514: $i] :
( ( in @ X514
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X513: $i] :
( ( in @ X513
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) ) )
| ( imp @ $false @ $false ) ) ) ) )
=> ( ( ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X513 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X514 ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41d]),c_0_43]),c_0_28]),c_0_44]),c_0_45]),c_0_46])]) ).
thf(c_0_48,plain,
! [X503: $i,X504: $i] :
( ( epred1_2 @ X504 @ X503 )
<=> ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) )
| ( imp @ $false @ $false ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_49,plain,
! [X637: $i,X638: $i] :
( ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X638 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X637 ) ) )
| ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X638
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X637
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])])]) ).
thf(c_0_50,plain,
! [X517: $i,X518: $i] :
( ( epred3_2 @ X518 @ X517 )
<=> ( ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ~ ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ~ ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_51,plain,
! [X503: $i,X504: $i] :
( ( epred1_2 @ X504 @ X503 )
=> ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) )
| ( imp @ $false @ $false ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_48]) ).
thf(c_0_52,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ $true
| ~ $true
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_53,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ $true
| ~ $true
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_54,plain,
! [X605: $i] :
( ( in @ X605
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X605 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X605 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X605 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X605 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz37]),c_0_43]),c_0_41]),c_0_45]) ).
thf(c_0_55,plain,
! [X517: $i,X518: $i] :
( ( epred3_2 @ X518 @ X517 )
=> ( ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ~ ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ~ ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_50]) ).
thf(c_0_56,plain,
! [X757: $i,X758: $i] :
( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $true @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $true @ $false )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $true @ $true )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $true @ $false )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $false @ $false )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $false @ $true )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $false @ $false )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $false @ $true )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X758 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X757 ) ) ) )
| ~ ( epred1_2 @ X758 @ X757 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])]) ).
thf(c_0_57,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_52]) ).
thf(c_0_58,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( imp @ ~ $true @ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_53]) ).
thf(c_0_59,plain,
! [X735: $i] :
( ~ ( in @ X735
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X735 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X735 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X735 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X735 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])]) ).
thf(c_0_60,negated_conjecture,
~ ! [X505: $i] :
( ( in @ X505
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X504: $i] :
( ( in @ X504
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X503: $i] :
( ( in @ X503
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X505 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X505 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X504 ) ) ) )
=> ( ( epred1_2 @ X504 @ X503 )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X505 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X505 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X503 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz51b])]),c_0_43]),c_0_45]),c_0_46]),c_0_42])]),c_0_48]) ).
thf(c_0_61,plain,
! [X761: $i,X762: $i] :
( ( $true
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $false )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $false )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $true )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $true )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $false )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $false )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $false )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $false )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $true )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $true )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $false )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $false )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $true )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $true )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $true @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ~ ( imp @ $false @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $false )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $false )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $true )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $true )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $false )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $false )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $false )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $false )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $true )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $true )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $false )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $false )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $true )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $true )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( $true
| ( imp @ $false @ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) )
& ( ~ $true
| ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X762 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X761 ) ) ) )
| ~ ( epred3_2 @ X762 @ X761 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])]) ).
thf(c_0_62,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_63,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_64,plain,
! [X4: $i,X1: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(cn,[status(thm)],[c_0_57]) ).
thf(c_0_65,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(cn,[status(thm)],[c_0_58]) ).
thf(c_0_66,plain,
! [X1: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_67,negated_conjecture,
( ( in @ esk1_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
& ( in @ esk2_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
& ( in @ esk3_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
& ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) ) )
& ( epred1_2 @ esk2_0 @ esk3_0 )
& ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])]) ).
thf(c_0_68,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_69,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ $true
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_70,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_71,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred1_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_62]) ).
thf(c_0_72,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(cn,[status(thm)],[c_0_63]) ).
thf(c_0_73,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(csr,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_74,plain,
! [X1: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[c_0_66]) ).
thf(c_0_75,negated_conjecture,
( in @ esk3_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_76,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_77,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_78,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ $true
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_79,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_68]) ).
thf(c_0_80,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(cn,[status(thm)],[c_0_69]) ).
thf(c_0_81,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_82,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ~ ( epred1_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_70]) ).
thf(c_0_83,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_71]) ).
thf(c_0_84,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_72]) ).
thf(c_0_85,plain,
! [X1: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_86,negated_conjecture,
( in @ esk3_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
inference(cn,[status(thm)],[c_0_75]) ).
thf(c_0_87,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_88,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( imp @ ~ $true @ ~ $true )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_89,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_90,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_76]) ).
thf(c_0_91,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_77]) ).
thf(c_0_92,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_78]) ).
thf(c_0_93,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_79]) ).
thf(c_0_94,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_80]) ).
thf(c_0_95,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred1_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_81]) ).
thf(c_0_96,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_82]) ).
thf(c_0_97,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[c_0_83,c_0_84]) ).
thf(c_0_98,negated_conjecture,
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( imp @ ~ $true @ $true ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_99,plain,
! [X519: $i,X520: $i] :
( ( epred4_2 @ X520 @ X519 )
<=> ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ~ ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ~ ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) ) ),
introduced(definition) ).
thf(c_0_100,plain,
! [X519: $i,X520: $i] :
( ( epred5_2 @ X520 @ X519 )
<=> ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) ),
introduced(definition) ).
thf(c_0_101,plain,
! [X515: $i,X516: $i] :
( ( epred2_2 @ X516 @ X515 )
<=> ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( imp @ $false @ $false ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_102,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_87]) ).
thf(c_0_103,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_88]) ).
thf(c_0_104,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred1_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_89]) ).
thf(c_0_105,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_106,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_90]) ).
thf(c_0_107,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_91]) ).
thf(c_0_108,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_92]) ).
thf(c_0_109,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[c_0_93,c_0_94]) ).
thf(c_0_110,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_95]) ).
thf(c_0_111,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]) ).
thf(c_0_112,plain,
! [X518: $i] :
( ( in @ X518
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X517: $i] :
( ( in @ X517
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X517 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X518 ) ) )
=> ( epred3_2 @ X518 @ X517 ) ) ) ),
inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41g]),c_0_43]),c_0_28]),c_0_44]),c_0_45]),c_0_46])]),c_0_50]) ).
thf(c_0_113,plain,
! [X520: $i] :
( ( in @ X520
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X519: $i] :
( ( in @ X519
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( ( epred4_2 @ X520 @ X519 )
& ( epred5_2 @ X520 @ X519 ) )
=> ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41k]),c_0_43]),c_0_28]),c_0_44]),c_0_45]),c_0_46])]),c_0_99]),c_0_100]) ).
thf(c_0_114,plain,
! [X519: $i,X520: $i] :
( ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ~ ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ~ ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
=> ( epred4_2 @ X520 @ X519 ) ),
inference(split_equiv,[status(thm)],[c_0_99]) ).
thf(c_0_115,plain,
! [X515: $i,X516: $i] :
( ( epred2_2 @ X516 @ X515 )
=> ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( imp @ $false @ $false ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_101]) ).
thf(c_0_116,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(cn,[status(thm)],[c_0_102]) ).
thf(c_0_117,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(cn,[status(thm)],[c_0_103]) ).
thf(c_0_118,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_104]) ).
thf(c_0_119,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_105]) ).
thf(c_0_120,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[c_0_106,c_0_107]) ).
thf(c_0_121,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_108,c_0_109]),c_0_94]) ).
thf(c_0_122,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ( imp @ ~ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_110]),c_0_111]) ).
thf(c_0_123,plain,
! [X641: $i,X642: $i] :
( ~ ( in @ X641
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X642
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X641 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X642 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X642 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X641 ) ) )
| ( epred3_2 @ X641 @ X642 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_112])])])]) ).
thf(c_0_124,plain,
! [X643: $i,X644: $i] :
( ~ ( in @ X643
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X644
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred4_2 @ X643 @ X644 )
| ~ ( epred5_2 @ X643 @ X644 )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X643 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X644 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X644 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X643 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_113])])])]) ).
thf(c_0_125,plain,
! [X512: $i] :
( ( in @ X512
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X511: $i] :
( ( in @ X511
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X510: $i] :
( ( in @ X510
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X511 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X512 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X512 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X511 ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X510 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X511 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X511 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X510 ) ) ) )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X510 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X512 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X512 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X510 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz50]),c_0_43]),c_0_45]),c_0_42]) ).
thf(c_0_126,plain,
! [X620: $i] :
( ( in @ X620
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X619: $i] :
( ( in @ X619
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X620 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X619 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X619 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X620 ) ) )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X620 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X619 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X619 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X620 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz42]),c_0_43]),c_0_44]),c_0_45]),c_0_42]) ).
thf(c_0_127,plain,
! [X763: $i,X764: $i] :
( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X763 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X764 ) ) )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $true @ $false )
| ~ $true
| ( epred4_2 @ X764 @ X763 ) )
& ( $true
| ~ ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) )
& ( ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred4_2 @ X764 @ X763 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_114])])])]) ).
thf(c_0_128,plain,
! [X759: $i,X760: $i] :
( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $true @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $true @ $false )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $true @ $true )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $true @ $false )
| $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $false @ $false )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $false @ $true )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $false @ $false )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $false @ $true )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X760 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X759 ) ) ) )
| ~ ( epred2_2 @ X760 @ X759 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])])]) ).
thf(c_0_129,plain,
! [X519: $i,X520: $i] :
( ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X519 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X520 ) ) )
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) )
=> ( epred5_2 @ X520 @ X519 ) ),
inference(split_equiv,[status(thm)],[c_0_100]) ).
thf(c_0_130,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_131,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[c_0_116,c_0_117]) ).
thf(c_0_132,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[c_0_118,c_0_84]) ).
thf(c_0_133,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_119]) ).
thf(c_0_134,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
thf(c_0_135,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_110]),c_0_98]),c_0_122]) ).
thf(c_0_136,plain,
! [X4: $i,X1: $i] :
( ( epred3_2 @ X1 @ X4 )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
thf(c_0_137,plain,
! [X1: $i,X4: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred4_2 @ X1 @ X4 )
| ~ ( epred5_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
thf(c_0_138,plain,
! [X634: $i,X635: $i,X636: $i] :
( ~ ( in @ X634
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X635
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X636
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X635 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X634 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X634 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X635 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X636 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X635 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X635 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X636 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X636 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X634 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X634 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X636 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])])]) ).
thf(c_0_139,plain,
! [X749: $i,X750: $i] :
( ~ ( in @ X749
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X750
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X749 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X750 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X750 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X749 ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X749 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X750 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X750 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X749 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_126])])])]) ).
thf(c_0_140,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ $true @ ~ $true )
| ( imp @ $true @ $true )
| ( epred4_2 @ X4 @ X1 )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
thf(c_0_141,plain,
! [X1: $i,X4: $i] :
( ( epred4_2 @ X1 @ X4 )
| ~ ( imp @ $true @ ~ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
thf(c_0_142,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_143,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_144,plain,
! [X765: $i,X766: $i] :
( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X765 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X766 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( epred5_2 @ X766 @ X765 ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( epred5_2 @ X766 @ X765 ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( epred5_2 @ X766 @ X765 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])])])]) ).
thf(c_0_145,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred1_2 @ X1 @ X4 )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_130]) ).
thf(c_0_146,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
thf(c_0_147,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred1_2 @ X1 @ X4 )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_133]),c_0_134]),c_0_135]) ).
thf(c_0_148,plain,
! [X4: $i,X1: $i] :
( ( epred3_2 @ X1 @ X4 )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[c_0_136]) ).
thf(c_0_149,plain,
! [X1: $i,X4: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred4_2 @ X1 @ X4 )
| ~ ( epred5_2 @ X1 @ X4 ) ),
inference(cn,[status(thm)],[c_0_137]) ).
thf(c_0_150,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
thf(c_0_151,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
thf(c_0_152,plain,
! [X622: $i] :
( ( in @ X622
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X621: $i] :
( ( in @ X621
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X621 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X622 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X622 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X621 ) ) ) )
=> ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X621 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X622 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X622 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X621 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz43]),c_0_43]),c_0_44]),c_0_45]),c_0_42]) ).
thf(c_0_153,plain,
! [X4: $i,X1: $i] :
( ( epred4_2 @ X4 @ X1 )
| ( imp @ $true @ $true )
| ( imp @ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_140]) ).
thf(c_0_154,plain,
! [X1: $i,X4: $i] :
( ( epred4_2 @ X1 @ X4 )
| ~ ( imp @ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_141]) ).
thf(c_0_155,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_156,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred2_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_142]) ).
thf(c_0_157,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(cn,[status(thm)],[c_0_143]) ).
thf(c_0_158,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_159,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ( epred5_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_160,plain,
! [X1: $i,X4: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_161,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ( epred5_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_162,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ $true @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_163,plain,
! [X4: $i,X1: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( epred5_2 @ X4 @ X1 )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( imp @ $true @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_164,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(cn,[status(thm)],[c_0_145]) ).
thf(c_0_165,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ ( imp @ $true @ $true )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_133]),c_0_98]) ).
thf(c_0_166,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ $true @ $true )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_135,c_0_146]) ).
thf(c_0_167,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ~ ( epred1_2 @ X1 @ X4 )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_147,c_0_146]) ).
thf(c_0_168,plain,
! [X1: $i,X4: $i] :
( ( epred3_2 @ X1 @ X4 )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred4_2 @ X1 @ X4 )
| ~ ( epred5_2 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
thf(c_0_169,negated_conjecture,
( in @ esk2_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_170,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[c_0_150]) ).
thf(c_0_171,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[c_0_151]) ).
thf(c_0_172,negated_conjecture,
( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_173,negated_conjecture,
( in @ esk1_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_174,plain,
! [X751: $i,X752: $i] :
( ~ ( in @ X751
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X752
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X752 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X751 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X751 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X752 ) ) ) )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X752 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X751 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X751 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X752 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_152])])])]) ).
thf(c_0_175,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X4 @ X1 )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_153]),c_0_154]) ).
thf(c_0_176,plain,
! [X516: $i] :
( ( in @ X516
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X515: $i] :
( ( in @ X515
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( ( ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X515 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X516 ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
=> ( epred2_2 @ X516 @ X515 ) ) ) ),
inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41e]),c_0_43]),c_0_28]),c_0_44]),c_0_45]),c_0_46])]),c_0_101]) ).
thf(c_0_177,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ $true )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ $true
| ~ ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_178,plain,
! [X509: $i] :
( ( in @ X509
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X508: $i] :
( ( in @ X508
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X507: $i] :
( ( in @ X507
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X506: $i] :
( ( in @ X506
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X508 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X509 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X509 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X508 ) ) ) )
=> ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X509 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X507 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X507 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X509 ) ) )
=> ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X508 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X506 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X506 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X508 ) ) )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X506 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X507 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X507 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X506 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz45]),c_0_43]),c_0_41]),c_0_45]),c_0_42]) ).
thf(c_0_179,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ~ ( epred2_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_155]) ).
thf(c_0_180,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_156]) ).
thf(c_0_181,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_157]) ).
thf(c_0_182,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ~ ( epred2_2 @ X1 @ X4 )
| ~ ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_158]) ).
thf(c_0_183,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X1 @ X4 )
| ( imp @ ~ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_159]) ).
thf(c_0_184,plain,
! [X1: $i,X4: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_160]) ).
thf(c_0_185,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X1 @ X4 )
| ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_161]) ).
thf(c_0_186,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_162]) ).
thf(c_0_187,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X4 @ X1 )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_163]) ).
thf(c_0_188,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_84]),c_0_111]) ).
thf(c_0_189,negated_conjecture,
epred1_2 @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_190,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_146]),c_0_166]),c_0_167]) ).
thf(c_0_191,negated_conjecture,
! [X1: $i] :
( ( epred3_2 @ X1 @ esk3_0 )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred4_2 @ X1 @ esk3_0 )
| ~ ( epred5_2 @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_168,c_0_86]) ).
thf(c_0_192,negated_conjecture,
( in @ esk2_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
inference(cn,[status(thm)],[c_0_169]) ).
thf(c_0_193,negated_conjecture,
~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_194,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
thf(c_0_195,negated_conjecture,
( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) ) ),
inference(cn,[status(thm)],[c_0_172]) ).
thf(c_0_196,negated_conjecture,
( in @ esk1_0
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ),
inference(cn,[status(thm)],[c_0_173]) ).
thf(c_0_197,plain,
! [X1: $i,X4: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_174]) ).
thf(c_0_198,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ $true )
| ( epred4_2 @ X4 @ X1 )
| ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
<~> ( imp @ $true @ $true ) )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(ext_eqfact,[status(thm)],[c_0_175]) ).
thf(c_0_199,plain,
! [X639: $i,X640: $i] :
( ( ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| $true
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X640 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X639 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( epred2_2 @ X639 @ X640 )
| ~ ( in @ X640
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X639
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_176])])])])]) ).
thf(c_0_200,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred3_2 @ X1 @ X4 )
| ~ ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_177]) ).
thf(c_0_201,plain,
! [X630: $i,X631: $i,X632: $i,X633: $i] :
( ~ ( in @ X630
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X631
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X632
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X633
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X631 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X630 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X630 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X631 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X630 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X632 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X632 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X630 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X631 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X633 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X633 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X631 ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X633 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X632 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X632 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X633 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_178])])])]) ).
thf(c_0_202,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_179]) ).
thf(c_0_203,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[c_0_180,c_0_181]) ).
thf(c_0_204,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_182]) ).
thf(c_0_205,plain,
! [X1: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( epred5_2 @ X4 @ X1 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_183]),c_0_184]) ).
thf(c_0_206,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( epred5_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[c_0_185]),c_0_184]) ).
thf(c_0_207,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ $true ) ),
inference(cn,[status(thm)],[c_0_186]) ).
thf(c_0_208,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( epred5_2 @ X1 @ X4 )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( imp @ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_187]) ).
thf(c_0_209,negated_conjecture,
( ( imp @ $true @ ~ $true )
| ( imp @ ~ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
thf(c_0_210,negated_conjecture,
( ( imp @ $true @ ~ $true )
| ~ ( epred3_2 @ esk2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_190,c_0_189]) ).
thf(c_0_211,negated_conjecture,
( ( epred3_2 @ esk2_0 @ esk3_0 )
| ~ ( epred4_2 @ esk2_0 @ esk3_0 )
| ~ ( epred5_2 @ esk2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
thf(c_0_212,negated_conjecture,
~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) ) ) ),
inference(cn,[status(thm)],[c_0_193]) ).
thf(c_0_213,negated_conjecture,
! [X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_192]),c_0_196])]) ).
thf(c_0_214,plain,
! [X1: $i,X4: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[c_0_197]) ).
thf(c_0_215,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X4 @ X1 )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_198])])]) ).
thf(c_0_216,plain,
! [X4: $i,X1: $i] :
( ( epred2_2 @ X1 @ X4 )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
thf(c_0_217,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred3_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_200]) ).
thf(c_0_218,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X4 @ X1 )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( imp @ $true @ ~ $true )
| ~ ( imp @ $true @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
thf(c_0_219,plain,
! [X1: $i,X6: $i,X5: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X6 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X6 ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X6
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X6 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X6 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_201]) ).
thf(c_0_220,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_98]) ).
thf(c_0_221,plain,
! [X1: $i,X4: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_206]),c_0_207]) ).
thf(c_0_222,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( epred5_2 @ X1 @ X4 )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_181]),c_0_209]),c_0_184]) ).
thf(c_0_223,negated_conjecture,
( ( imp @ $true @ ~ $true )
| ~ ( epred4_2 @ esk2_0 @ esk3_0 )
| ~ ( epred5_2 @ esk2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_210,c_0_211]) ).
thf(c_0_224,negated_conjecture,
~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_86])]) ).
thf(c_0_225,plain,
! [X1: $i,X4: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ $true )
| ( epred4_2 @ X4 @ X1 )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_214,c_0_215]) ).
thf(c_0_226,plain,
! [X4: $i,X1: $i] :
( ( epred2_2 @ X1 @ X4 )
| ~ ( imp @ $true @ ~ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_216]) ).
thf(c_0_227,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_109]),c_0_134]) ).
thf(c_0_228,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X4 @ X1 )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_218]) ).
thf(c_0_229,plain,
! [X1: $i,X4: $i,X5: $i,X6: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X6 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X6 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X6 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X6 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X6
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[c_0_219]) ).
thf(c_0_230,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_204,c_0_171]) ).
thf(c_0_231,plain,
! [X1: $i,X4: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_203]),c_0_220]) ).
thf(c_0_232,plain,
! [X1: $i,X4: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ $true )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
thf(c_0_233,plain,
( ( imp @ $true @ ~ $true )
| ~ ( epred4_2 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_184]),c_0_209]) ).
thf(c_0_234,plain,
( ( epred4_2 @ esk2_0 @ esk3_0 )
| ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_86]),c_0_192])]) ).
thf(c_0_235,plain,
! [X4: $i,X1: $i] :
( ( epred2_2 @ X1 @ X4 )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_226]) ).
thf(c_0_236,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ( epred5_2 @ X1 @ X4 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_205]),c_0_227]),c_0_134]),c_0_184]) ).
thf(c_0_237,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( epred5_2 @ X1 @ X4 )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_94]),c_0_209]),c_0_184]) ).
thf(c_0_238,plain,
! [X1: $i,X4: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_228]) ).
thf(c_0_239,negated_conjecture,
! [X1: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_195]),c_0_192]),c_0_196])]) ).
thf(c_0_240,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred2_2 @ X1 @ X4 )
| ~ ( epred5_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_149]),c_0_154]) ).
thf(c_0_241,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ( epred5_2 @ X1 @ X4 )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_222]),c_0_232]),c_0_184]) ).
thf(c_0_242,plain,
( ( imp @ $true @ $true )
| ( imp @ $true @ ~ $true ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_209]) ).
thf(c_0_243,plain,
! [X1: $i,X4: $i] :
( ( epred2_2 @ X1 @ X4 )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred5_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_149]),c_0_154]) ).
thf(c_0_244,plain,
! [X1: $i,X4: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( epred5_2 @ X4 @ X1 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(spm,[status(thm)],[c_0_214,c_0_205]) ).
thf(c_0_245,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ $true )
| ( epred5_2 @ X1 @ X4 )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
thf(c_0_246,negated_conjecture,
~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_171]),c_0_196]),c_0_86])]) ).
thf(c_0_247,plain,
! [X4: $i,X1: $i] :
( ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
<~> ( imp @ ~ $true @ ~ $true ) )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(ext_eqfact,[status(thm)],[c_0_97]) ).
thf(c_0_248,plain,
! [X1: $i,X4: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_238,c_0_171]) ).
thf(c_0_249,negated_conjecture,
( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk3_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_239]),c_0_86]),c_0_196])]) ).
thf(c_0_250,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( epred5_2 @ X1 @ X4 )
| ~ ( epred1_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_84]),c_0_209]),c_0_184]) ).
thf(c_0_251,plain,
! [X1: $i] :
( ( imp @ $true @ $true )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred2_2 @ X1 @ X1 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_74]),c_0_241]),c_0_242]) ).
thf(c_0_252,negated_conjecture,
! [X1: $i] :
( ( epred2_2 @ X1 @ esk3_0 )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred5_2 @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_243,c_0_86]) ).
thf(c_0_253,plain,
! [X1: $i,X4: $i] :
( ( epred5_2 @ X1 @ X4 )
| ( epred3_2 @ X4 @ X1 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(spm,[status(thm)],[c_0_148,c_0_244]) ).
thf(c_0_254,plain,
! [X1: $i,X4: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ $true )
| ~ ( epred3_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_237]),c_0_245]) ).
thf(c_0_255,negated_conjecture,
( ~ ( epred4_2 @ esk3_0 @ esk1_0 )
| ~ ( epred5_2 @ esk3_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_149]),c_0_196]),c_0_86])]) ).
thf(c_0_256,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_247])])]) ).
thf(c_0_257,plain,
! [X527: $i] :
( ( in @ X527
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X526: $i] :
( ( in @ X526
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ! [X525: $i] :
( ( in @ X525
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
=> ( ( ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $true @ $true ) )
& ( ~ $true
| ~ ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) ) ) )
| ( ( ~ ~ $true
| ~ ( imp @ $false @ $true ) )
& ( ~ $true
| ~ ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) ) )
| ( imp @ $true @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) ) )
| ( imp @ $true @ $false ) ) ) )
& ( ( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $true @ $true ) )
& ( ~ $true
| ( imp @ $true @ $false ) ) ) )
& ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) ) ) )
| ( ( ~ ~ $true
| ( imp @ $false @ $true ) )
& ( ~ $true
| ( imp @ $false @ $false ) ) ) ) )
| ( ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) ) )
| ( imp @ $false @ $true ) )
& ( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) ) )
| ( imp @ $false @ $false ) ) ) ) )
=> ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X525 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X526 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X525 ) ) ) )
=> ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X525 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X527 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X525 ) ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz51a]),c_0_43]),c_0_45]),c_0_46]),c_0_42])]) ).
thf(c_0_258,plain,
! [X4: $i,X1: $i] :
( ( epred5_2 @ X1 @ X4 )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred5_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_149]),c_0_154]) ).
thf(c_0_259,plain,
( ( epred5_2 @ esk2_0 @ esk3_0 )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_189])]) ).
thf(c_0_260,negated_conjecture,
( ( imp @ $true @ $true )
| ~ ( epred2_2 @ esk3_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_251,c_0_86]) ).
thf(c_0_261,negated_conjecture,
( ( epred2_2 @ esk3_0 @ esk3_0 )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred5_2 @ esk3_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_252,c_0_86]) ).
thf(c_0_262,plain,
! [X1: $i] :
( ( epred5_2 @ X1 @ X1 )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_74]),c_0_254]) ).
thf(c_0_263,plain,
( ~ ( epred4_2 @ esk3_0 @ esk1_0 )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_255,c_0_184]) ).
thf(c_0_264,plain,
! [X4: $i,X1: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ ~ $true @ ~ $true )
| ( imp @ ~ $true @ $true )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred1_2 @ X4 @ X1 ) ),
inference(spm,[status(thm)],[c_0_214,c_0_256]) ).
thf(c_0_265,plain,
! [X649: $i,X650: $i,X651: $i] :
( ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| $true
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ~ $true
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( imp @ $false @ $false )
| ( imp @ $false @ $true )
| ( imp @ $true @ $false )
| ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| $true
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ $true
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( $true
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) ) )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) )
& ( ~ ( imp @ $false @ $false )
| ~ ( imp @ $false @ $true )
| ~ ( imp @ $true @ $false )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X650 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X649 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X651 ) ) ) )
| ~ ( in @ X651
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X650
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X649
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_257])])])])]) ).
thf(c_0_266,negated_conjecture,
! [X1: $i] :
( ( epred5_2 @ esk3_0 @ X1 )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred5_2 @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_258,c_0_86]) ).
thf(c_0_267,plain,
epred5_2 @ esk2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_74]),c_0_196])]) ).
thf(c_0_268,negated_conjecture,
( ( imp @ $true @ $true )
| ~ ( epred5_2 @ esk3_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_242]) ).
thf(c_0_269,negated_conjecture,
( ( epred5_2 @ esk3_0 @ esk3_0 )
| ~ ( imp @ ~ $true @ $true ) ),
inference(spm,[status(thm)],[c_0_262,c_0_86]) ).
thf(c_0_270,plain,
( ~ ( imp @ ~ $true @ ~ $true )
| ~ ( imp @ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_263,c_0_154]) ).
thf(c_0_271,plain,
( ( imp @ ~ $true @ $true )
| ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_264]),c_0_86]),c_0_192]),c_0_189])]) ).
thf(c_0_272,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
thf(c_0_273,negated_conjecture,
( ~ ( epred4_2 @ esk3_0 @ esk2_0 )
| ~ ( epred5_2 @ esk3_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_149]),c_0_192]),c_0_86])]) ).
thf(c_0_274,negated_conjecture,
( ( epred5_2 @ esk3_0 @ esk2_0 )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ ~ $true ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_192]),c_0_267])]) ).
thf(c_0_275,negated_conjecture,
( ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ $true ) ),
inference(spm,[status(thm)],[c_0_268,c_0_269]) ).
thf(c_0_276,plain,
( ( imp @ ~ $true @ $true )
| ~ ( imp @ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_270,c_0_271]) ).
thf(c_0_277,plain,
! [X1: $i,X4: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
thf(c_0_278,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ $true
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_279,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_272]) ).
thf(c_0_280,negated_conjecture,
( ~ ( imp @ $true @ $true )
| ~ ( imp @ $true @ ~ $true ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_274]),c_0_154]) ).
thf(c_0_281,plain,
imp @ $true @ $true,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_242]) ).
thf(c_0_282,plain,
! [X4: $i,X1: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( epred2_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ $true
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_199]) ).
thf(c_0_283,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ $true
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_284,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred2_2 @ X1 @ X4 )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_277]) ).
thf(c_0_285,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_278]) ).
thf(c_0_286,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ~ $true
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_287,plain,
! [X5: $i,X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_279]) ).
thf(c_0_288,negated_conjecture,
~ ( imp @ $true @ ~ $true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_280,c_0_281])]) ).
thf(c_0_289,plain,
! [X4: $i,X1: $i] :
( ( epred2_2 @ X1 @ X4 )
| ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[c_0_282]) ).
thf(c_0_290,plain,
! [X1: $i,X4: $i] :
( ( imp @ $true @ ~ $true )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_283]) ).
thf(c_0_291,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( imp @ ~ $true @ ~ $true )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[c_0_284]) ).
thf(c_0_292,plain,
! [X1: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_285]) ).
thf(c_0_293,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ $true )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) ),
inference(cn,[status(thm)],[c_0_286]) ).
thf(c_0_294,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(csr,[status(thm)],[c_0_287,c_0_170]) ).
thf(c_0_295,negated_conjecture,
imp @ ~ $true @ ~ $true,
inference(sr,[status(thm)],[c_0_209,c_0_288]) ).
thf(c_0_296,plain,
! [X4: $i,X1: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( epred2_2 @ X1 @ X4 )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_289]) ).
thf(c_0_297,plain,
! [X4: $i,X1: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_290]) ).
thf(c_0_298,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(csr,[status(thm)],[c_0_291,c_0_181]) ).
thf(c_0_299,plain,
! [X1: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(csr,[status(thm)],[c_0_292,c_0_270]) ).
thf(c_0_300,plain,
! [X4: $i,X1: $i] :
( ( imp @ $true @ ~ $true )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ $true @ $true )
| ~ ( imp @ ~ $true @ $true ) ),
inference(cn,[status(thm)],[c_0_293]) ).
thf(c_0_301,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X5 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X5
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_294,c_0_281])]),c_0_295])]) ).
thf(c_0_302,plain,
! [X4: $i,X1: $i] :
( ( epred2_2 @ X1 @ X4 )
| ( epred3_2 @ X1 @ X4 )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_148,c_0_296]) ).
thf(c_0_303,plain,
! [X4: $i,X1: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(csr,[status(thm)],[c_0_297,c_0_270]) ).
thf(c_0_304,plain,
! [X4: $i,X1: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ $true @ ~ $true )
| ( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
<~> ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(ext_eqfact,[status(thm)],[c_0_298]) ).
thf(c_0_305,plain,
! [X1: $i,X4: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_299,c_0_281])]),c_0_295])]) ).
thf(c_0_306,plain,
! [X4: $i,X1: $i] :
( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ $true ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_300,c_0_281])]),c_0_288]) ).
thf(c_0_307,negated_conjecture,
! [X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_195]),c_0_192]),c_0_196])]) ).
thf(c_0_308,negated_conjecture,
! [X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_195]),c_0_192]),c_0_196])]) ).
thf(c_0_309,negated_conjecture,
! [X1: $i] :
( ( epred3_2 @ X1 @ esk3_0 )
| ( epred2_2 @ X1 @ esk3_0 )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_302,c_0_86]) ).
thf(c_0_310,plain,
! [X4: $i,X1: $i] :
( ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_303,c_0_295])]) ).
thf(c_0_311,plain,
! [X4: $i,X1: $i] :
( ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) ) )
| ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) ) )
| ( imp @ $true @ ~ $true )
| ~ ( epred2_2 @ X4 @ X1 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_304])])]) ).
thf(c_0_312,plain,
! [X1: $i,X4: $i] :
( ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_305]),c_0_288]),c_0_306]) ).
thf(c_0_313,negated_conjecture,
! [X1: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) )
| ~ ( n_some
@ ( diffprop
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_307]),c_0_192])]) ).
thf(c_0_314,negated_conjecture,
! [X1: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) )
| ~ ( n_is
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk1_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_308]),c_0_192])]) ).
thf(c_0_315,negated_conjecture,
( ( epred2_2 @ esk2_0 @ esk3_0 )
| ( epred3_2 @ esk2_0 @ esk3_0 )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(spm,[status(thm)],[c_0_309,c_0_192]) ).
thf(c_0_316,plain,
! [X1: $i,X4: $i] :
( ~ ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X4 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) ) )
| ~ ( in @ X4
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred2_2 @ X1 @ X4 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_310,c_0_311]),c_0_288]),c_0_312]) ).
thf(c_0_317,plain,
! [X1: $i] :
( ( d_29_ii
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( ap
@ ( times
@ ( first1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ X1 ) )
@ ( second1
@ ( d_Sep @ omega
@ ^ [Z0: $i] : ( Z0 != emptyset ) )
@ esk2_0 ) ) )
| ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred2_2 @ X1 @ esk1_0 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_311]),c_0_288]),c_0_314]) ).
thf(c_0_318,negated_conjecture,
( ( epred2_2 @ esk2_0 @ esk3_0 )
| ~ ( imp @ $true @ ~ $true )
| ~ ( epred5_2 @ esk2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_252,c_0_192]) ).
thf(c_0_319,negated_conjecture,
( ( epred2_2 @ esk2_0 @ esk3_0 )
| ( imp @ $true @ ~ $true ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_315]),c_0_209]) ).
thf(c_0_320,negated_conjecture,
( ( epred2_2 @ esk3_0 @ esk1_0 )
| ~ ( imp @ ~ $true @ ~ $true ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_296]),c_0_196]),c_0_86])]) ).
thf(c_0_321,plain,
! [X1: $i] :
( ~ ( in @ X1
@ ( d_Pi @ ( d_1to @ n_2 )
@ ^ [Z0: $i] :
( d_Sep @ omega
@ ^ [Z1: $i] : ( Z1 != emptyset ) ) ) )
| ~ ( epred2_2 @ esk2_0 @ X1 )
| ~ ( epred2_2 @ X1 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_317]),c_0_192])]) ).
thf(c_0_322,negated_conjecture,
epred2_2 @ esk2_0 @ esk3_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_318,c_0_267])]),c_0_319]) ).
thf(c_0_323,negated_conjecture,
epred2_2 @ esk3_0 @ esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_320,c_0_295])]) ).
thf(c_0_324,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_321,c_0_86]),c_0_322]),c_0_323])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.15 % Problem : NUM743^4 : TPTP v8.1.2. Released v7.1.0.
% 0.05/0.16 % Command : run_E %s %d THM
% 0.16/0.36 % Computer : n015.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 09:46:51 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.21/0.52 Running higher-order theorem proving
% 0.21/0.52 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ujmERprOuX/E---3.1_22739.p
% 90.13/11.95 # Version: 3.1.0-ho
% 90.13/11.95 # Preprocessing class: HSLMSMSMLLLCHSA.
% 90.13/11.95 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 90.13/11.95 # Starting pre_casc_4 with 1200s (4) cores
% 90.13/11.95 # Starting full_lambda_6 with 300s (1) cores
% 90.13/11.95 # Starting sh10 with 300s (1) cores
% 90.13/11.95 # Starting post_as_ho9 with 300s (1) cores
% 90.13/11.95 # Starting post_as_ho8 with 300s (1) cores
% 90.13/11.95 # post_as_ho9 with pid 22821 completed with status 0
% 90.13/11.95 # Result found by post_as_ho9
% 90.13/11.95 # Preprocessing class: HSLMSMSMLLLCHSA.
% 90.13/11.95 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 90.13/11.95 # Starting pre_casc_4 with 1200s (4) cores
% 90.13/11.95 # Starting full_lambda_6 with 300s (1) cores
% 90.13/11.95 # Starting sh10 with 300s (1) cores
% 90.13/11.95 # Starting post_as_ho9 with 300s (1) cores
% 90.13/11.95 # SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 90.13/11.95 # Search class: HGUNF-FSLM21-DHSMMFBN
% 90.13/11.95 # partial match(5): HGUSM-FSLM31-DHSFFFBN
% 90.13/11.95 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 90.13/11.95 # Starting new_bool_5 with 135s (1) cores
% 90.13/11.95 # new_bool_5 with pid 22830 completed with status 0
% 90.13/11.95 # Result found by new_bool_5
% 90.13/11.95 # Preprocessing class: HSLMSMSMLLLCHSA.
% 90.13/11.95 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 90.13/11.95 # Starting pre_casc_4 with 1200s (4) cores
% 90.13/11.95 # Starting full_lambda_6 with 300s (1) cores
% 90.13/11.95 # Starting sh10 with 300s (1) cores
% 90.13/11.95 # Starting post_as_ho9 with 300s (1) cores
% 90.13/11.95 # SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 90.13/11.95 # Search class: HGUNF-FSLM21-DHSMMFBN
% 90.13/11.95 # partial match(5): HGUSM-FSLM31-DHSFFFBN
% 90.13/11.95 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 90.13/11.95 # Starting new_bool_5 with 135s (1) cores
% 90.13/11.95 # Preprocessing time : 0.017 s
% 90.13/11.95 # Presaturation interreduction done
% 90.13/11.95
% 90.13/11.95 # Proof found!
% 90.13/11.95 # SZS status Theorem
% 90.13/11.95 # SZS output start CNFRefutation
% See solution above
% 90.50/11.98 # Parsed axioms : 566
% 90.50/11.98 # Removed by relevancy pruning/SinE : 499
% 90.50/11.98 # Initial clauses : 12081
% 90.50/11.98 # Removed in clause preprocessing : 11670
% 90.50/11.98 # Initial clauses in saturation : 411
% 90.50/11.98 # Processed clauses : 7140
% 90.50/11.98 # ...of these trivial : 70
% 90.50/11.98 # ...subsumed : 4213
% 90.50/11.98 # ...remaining for further processing : 2857
% 90.50/11.98 # Other redundant clauses eliminated : 0
% 90.50/11.98 # Clauses deleted for lack of memory : 0
% 90.50/11.98 # Backward-subsumed : 958
% 90.50/11.98 # Backward-rewritten : 757
% 90.50/11.98 # Generated clauses : 52959
% 90.50/11.98 # ...of the previous two non-redundant : 31624
% 90.50/11.98 # ...aggressively subsumed : 0
% 90.50/11.98 # Contextual simplify-reflections : 800
% 90.50/11.98 # Paramodulations : 37686
% 90.50/11.98 # Factorizations : 0
% 90.50/11.98 # NegExts : 0
% 90.50/11.98 # Equation resolutions : 0
% 90.50/11.98 # Disequality decompositions : 0
% 90.50/11.98 # Total rewrite steps : 29258
% 90.50/11.98 # ...of those cached : 29192
% 90.50/11.98 # Propositional unsat checks : 0
% 90.50/11.98 # Propositional check models : 0
% 90.50/11.98 # Propositional check unsatisfiable : 0
% 90.50/11.98 # Propositional clauses : 0
% 90.50/11.98 # Propositional clauses after purity: 0
% 90.50/11.98 # Propositional unsat core size : 0
% 90.50/11.98 # Propositional preprocessing time : 0.000
% 90.50/11.98 # Propositional encoding time : 0.000
% 90.50/11.98 # Propositional solver time : 0.000
% 90.50/11.98 # Success case prop preproc time : 0.000
% 90.50/11.98 # Success case prop encoding time : 0.000
% 90.50/11.98 # Success case prop solver time : 0.000
% 90.50/11.98 # Current number of processed clauses : 812
% 90.50/11.98 # Positive orientable unit clauses : 35
% 90.50/11.98 # Positive unorientable unit clauses: 0
% 90.50/11.98 # Negative unit clauses : 19
% 90.50/11.98 # Non-unit-clauses : 758
% 90.50/11.98 # Current number of unprocessed clauses: 17012
% 90.50/11.98 # ...number of literals in the above : 137279
% 90.50/11.98 # Current number of archived formulas : 0
% 90.50/11.98 # Current number of archived clauses : 2045
% 90.50/11.98 # Clause-clause subsumption calls (NU) : 3361131
% 90.50/11.98 # Rec. Clause-clause subsumption calls : 192479
% 90.50/11.98 # Non-unit clause-clause subsumptions : 5424
% 90.50/11.98 # Unit Clause-clause subsumption calls : 21547
% 90.50/11.98 # Rewrite failures with RHS unbound : 0
% 90.50/11.98 # BW rewrite match attempts : 214
% 90.50/11.98 # BW rewrite match successes : 53
% 90.50/11.98 # Condensation attempts : 7140
% 90.50/11.98 # Condensation successes : 1
% 90.50/11.98 # Termbank termtop insertions : 6620258
% 90.50/11.98 # Search garbage collected termcells : 99032
% 90.50/11.98
% 90.50/11.98 # -------------------------------------------------
% 90.50/11.98 # User time : 11.153 s
% 90.50/11.98 # System time : 0.104 s
% 90.50/11.98 # Total time : 11.257 s
% 90.50/11.98 # Maximum resident set size: 33676 pages
% 90.50/11.98
% 90.50/11.98 # -------------------------------------------------
% 90.50/11.98 # User time : 11.172 s
% 90.50/11.98 # System time : 0.136 s
% 90.50/11.98 # Total time : 11.308 s
% 90.50/11.98 # Maximum resident set size: 8836 pages
% 90.50/11.98 % E---3.1 exiting
% 90.51/11.99 % E exiting
%------------------------------------------------------------------------------